Transmission lines

Discussion in 'Homework Help' started by Biggsy100, Mar 16, 2015.

  1. Biggsy100

    Thread Starter Member

    Apr 7, 2014
    88
    1

    1. The characteristic impedance of a transmission line is given by the equation:



    [​IMG]zo = R + jwL W G + jwC


    A transmission line-under-test has the following primary constants:


    L = 100 x 10-9 Henries per metre

    R = 4 x 10-3 Ohms per metre

    G = 1 x 10-7 Siemens per metre

    C = 20 x 10^-2 Farads per metre


    Calculate the magnitude of the characteristic impedance with an 8 kHz line
    signal frequency. Comment on the result and mention any reasonable
    assumptions made in your solution.


    [​IMG]
    [​IMG]

    1. Am I correct to square root this equation?
    2. Now I have completed the equation, should I have broken it down into stages to reach a resolution?
     
  2. MrChips

    Moderator

    Oct 2, 2009
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  3. Biggsy100

    Thread Starter Member

    Apr 7, 2014
    88
    1
    I am not sure why I would want to square root it at all, that is why I asked?

    On your picture it shows the how equation square rooted? I assumed that's what I had to do here? Are you suggesting from your notes that you supplied (many thanks) that I follow the whole process?
     
  4. MrChips

    Moderator

    Oct 2, 2009
    12,415
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    You cannot just take the square root of one side of an equation willy nilly.

    Here is a simple example:

    Distance travelled = velocity/time

    If I were to square the right-hand side of the equation for whatever whim, that would result in (velocity/time) squared which would give area as the result. Obviously, distance cannot be equal to area.

    The dimensions of (j\omega L + R) are Ohms.
    The dimensions of \frac{1}{(j\omega C + G) are Ohms.

    Hence when we take the product the result is in  Ohms^2.

    Taking the square root makes the equation dimensionally balanced.
     
  5. Biggsy100

    Thread Starter Member

    Apr 7, 2014
    88
    1
    So I square root the answer?
     
  6. MrChips

    Moderator

    Oct 2, 2009
    12,415
    3,354
    If this is your equation, no, you cannot take the square root.

    zo = R + jwL W G + jwC

    If you examine this equation you will notice that this equation is dimensionally unbalanced and therefore incorrect.

    The dimensions of jωC are not Ohms.

    I suggest you review the notes in the link provided and find the proper equation.

    The lesson here is: check the dimensions of both sides of the equation.
     
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